A further 800,000 homes will be put out of reach of people on housing benefit because of government welfare cuts – leaving low income families the choice of cutting spending on food to pay the rent or moving out, according to a study by housing experts.

The Chartered Institute of Housing has found there will be thousands more claimants than properties that are affordable on benefits alone, raising the possibility that the poor will migrate to "benefit ghettoes" in seaside towns or the north of England.

From this month, the government has capped housing benefit payments to, for example, a maximum £250 a week on a two-bedroom home. The cut is compounded by the allowances being scaled back by pegging them to the bottom third of rents in any borough.

The result is that in many towns and cities there will not be enough affordable homes to rent for those claiming local housing allowance, the benefit paid to tenants of private landlords. The problem is most acute in central London, where in two of the country's richest boroughs – Westminster, and Kensington and Chelsea – more than 35,000 homes will at a stroke be put out of reach of people on housing benefit.

It is unlikely that the poor will be able migrate to cheaper parts of the capital: in Newham, east London, there will be twice as many claimants as there are low-cost homes. In Croydon, 17,000 people will be chasing 10,000 properties.

The effect will be felt not just in south-east England. Before today, Birmingham had more than 37,000 homes with rents affordable on welfare. Now 34,500 housing benefit claimants will be chasing 23,000 low-cost houses, according to the analysis, carried out for the Guardian. On the Mersey, 21,000 people collecting local housing allowance will only be able to afford 12,000 homes in Liverpool.

Because welfare is set at Westminster, the cuts will also be felt in Scotland. In Glasgow there will be a thousand more benefit recipients than there are properties which can be rented with the government's reduced housing subsidy.

Grainia Long, the interim chief executive of the institute, said the welfare changes will "see for the first time more people chasing homes than the market currently provides".

"The only option to stay might be to borrow more or simply stop buying essential items such as food," she said. "This will mean that more than 1.3 million private tenants face the new year with dread – facing an uncomfortable prospect of homelessness or debt."

While the government says the average loss in benefits is £12 a week, the analysts say that is equivalent to 18% of unemployment benefits. This average also masks regional variations: the rent subsidy for a three-bedroom property in Bath drops by £26 a week; in Derby, the cut is half that.

Long said the poor, especially in south-east England, could end up in "benefit ghettoes", sinks of social unrest in the most affluent part of the country. "The whole of the south-east is a sea of high rents punctuated only by a few small isolated low-cost islands … mainly old seaside towns such as Margate and Hastings where the once buoyant tourist trade has long since declined. But if claimants migrate to areas like these then this will create benefit ghettoes … the result is likely to be increased social problems and a breakdown in community cohesion."

Even where there are enough low-rent properties for the poor, benefit claimants face competition from others looking to live cheaply. This problem is acute in university towns and cities. Nottingham, Newcastle and Leeds all appear to have equal numbers of cheap rental properties and welfare recipients, but the poor compete with large numbers of students.

The changes will also see people forced to move from where jobs are to where there are far fewer, the institute warns. "The analysis shows that big cities where we expect to find most of the jobs and the most varied employment are the worst hit by the government changes. If this (is supposed) to help people in terms of getting them into work then it looks as if it will not succeed."

Charities said the analysis vindicated their warnings that the government's plan will cause homelessness. Leslie Morphy of the charity Crisis said: "The figures make clear that there will just not be enough properties anywhere that are affordable on these reduced benefit levels. With unemployment rising and more people relying on housing benefit, yet soaring demand for properties, the government's plans just don't add up – we urge them to stop and reconsider."

Labour says it supports the principle of the benefit cap but added: "The government has got to get the detail right otherwise it will simply clobber the poorest and put families on the street".

Liam Bryne, the shadow welfare and pensions secretary, said there was evidence the benefits cap had been "so badly thought through it could actually end up costing more by pushing up the costs of homelessness … it's time to go back to the drawing board."

The Department for Work and Pensions said housing benefit was unfair because some families on benefits had been able to live in homes that most working families not on benefits could not afford.

The department said: "Early indications are that people are not moving out of cities in their droves to cheaper rural areas. For the vast majority of areas except the most expensive parts of inner and central London, at least 30% of all private rental properties will be affordable. Our measures will place a lid on spiralling rents and local authorities will continue to work with tenants and landlords to negotiate down rents, which will in turn help to keep properties within reach."